Note: Descriptions are shown in the official language in which they were submitted.
CA 02909351 2015-10-13
Method and Device for the Co-Simulation of Two Sub-Systems
The invention relates to a method and to a simulation device for the co-
simulation of two
subsystems of an overall system, which are reciprocally coupled by coupling
variables.
To simulate an overall system, the overall system is often divided into
subsystems, which are
then individually simulated - this is then referred to as distributed
simulation or co-simulation.
This is done, for example, when the subsystems are simulated in different
simulation tools, or
when parallel computing on multiple kernels is strived for, or when a real-
time simulation (for
example, a hardware-in-the-loop (HiL) system) is to be connected to a real
automation
system for a test bench. A subsystem represents a submodel of the system to be
simulated,
including the associated numerical solving algorithm. The simulations of the
subsystems,
when linked to each other, then yield the simulation of the overall system. In
the simulation, a
certain operating point of the overall system is simulated, or operating
points of the
subsystems related thereto are simulated, in every simulation step. An
operating point
describes the behavior of the overall system at a particular point in time
here. In the
distributed simulation of an overall system, so called coupling variables are
exchanged
between the subsystems at certain, predefined points in time, and the
subsystems are solved
in defined time steps, referred to as coupling time steps, independently of
other subsystems.
At the end of a coupling time step, data is exchanged between the subsystems
to
synchronize to the subsystems.
In the case of reciprocal dependencies of subsystems, for example when a first
subsystem
requires an output of a second subsystem as the input, whereby the second
subsystem
requires an output of the first subsystem as the input, not all coupling
variables needed are
known at the beginning of the coupling time step and must be estimated by way
of
extrapolation. The temporal behavior of one or more systems (subsystems) is
predicted by
way of the extrapolation.
The coupling of submodels of the subsystems is typically carried out in co-
simulation based
on signal-based, polynomial extrapolation of the coupling variables. In
general, zero order
methods, and on rare occasions methods of a higher order (1st or 2nd), are
used for this
purpose. The output signal y is calculated based on the signal-based
extrapolation as a
function of the input signal x, which is to say y=f(x) - this is also referred
to as a single-input,
single-output (SISO) process. Extrapolating relevant coupling variables
introduces what is
known as a coupling error, which directly (negatively) impacts the quality of
the results of the
(co-)simulation. Since an extrapolation is carried out over coupling time
steps, the introduced
error corresponds to a "local discretization error." Discontinuities at the
coupling points in
time (due to incremental extrapolation) thus also negatively impact the
numerical solution of
the subsystems. To keep the coupling error small, sampling steps or exchange
intervals
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must be kept small, which results in high computing times and consequently is
not desirable.
However, the coupling error also causes a distortion of the coupling signal
and results in an
intrinsic time lag of the coupling signal (virtual dead time), which
negatively influences the
dynamic behavior of closed-loop systems (such as a control loop). However, the
exchange of
the coupling variables also results in additional, "real" dead times through
the use of
communication systems, for example, the exchange of data via bus systems such
as
FlexRay or CAN. These real dead times are typically considerably higher than
the virtual
dead times resulting from coupling.
EP 2 442 248 Al, for example, describes a signal-based coupling method for a
co-simulation
with error correction and coupling time step control. This allows the
extrapolation errors to be
considerably reduced by way of an error compensation method. Furthermore,
(virtual and
real) dead times which do not significantly exceed the coupling time step can
thus be
compensated for.
The problem with signal-based extrapolation methods is that they fail when the
extrapolation
is carried out over long time intervals, which is to say over multiple
coupling time steps. This
case occurs with real-time simulation of the overall system since typically
large dead times
(multiple coupling time steps) occur in this case due to measurement (ND
conversion),
signal processing, data transmission via communication media and so forth. In
the real-time
simulation, the coupling variables must be available at fixedly predefined
points in time
(coupling time step) since otherwise the real-time simulation aborts with an
error. A real-time
simulation is needed, for example, when at least one real-time system is
coupled (with
another real-time system or a non-real-time system), or when tasks are coupled
on a real-
time system.
It is therefore an object of the present invention to improve the
extrapolation of coupling
variables in co-simulation, in particular in such a way that an extrapolation
is also made
possible over long time intervals, which is to say also over multiple coupling
time steps, so
that real-time co-simulation also becomes possible.
The invention provides a method, and an associated simulation device, in which
a
mathematical model of the subsystems which is valid at the current operating
point of the
overall system is ascertained from input variables and/or measured variables
of the
subsystems based on a method of data-based model identification, and the
coupling
variables for a subsequent coupling time step are extrapolated from this model
and made
available to the subsystems. Since the time behavior of the subsystems for a
certain time
period (operating point) is known very well due to the model, extrapolation is
thus also
possible over multiple coupling time steps, which enables real-time co-
simulation. However,
this also allows real-time systems to continue to be operated error-free, even
in the absence
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of measured values over multiple coupling time steps, since these can be
reliably determined
by the model-based extrapolation. In addition, the model-based extrapolation
also allows
noisy signals to be processed.
According to an aspect of the present invention, there is provided a method of
co-simulating
two subsystems of an overall system, which are reciprocally coupled by way of
coupling
variables, the method comprising ascertaining a mathematical model of the
subsystems, which
is valid at the current operating point of the overall system, from at least
one of input variables
and measured variables of the subsystems with a method of data-based model
identification
and, from the model, the coupling variables are extrapolated for a subsequent
coupling time
step and made available to the subsystems.
According to another aspect of the present invention, there is provided a
simulation device for
co-simulation of at least two subsystems of an overall system, which are
reciprocally coupled
by way of coupling variables, comprising at least one extrapolation unit which
receives at least
one of input variables and measured variables of the subsystems and, based
thereon, identifies
a mathematical model of the subsystems which is valid at the current operating
point of the
overall system based on a method of data-based model identification in order
to calculate the
coupling variables using the model.
The real and the virtual dead time can very easily be compensated for by
calculating
coupling variables that lie further ahead in the future by the dead time from
the model by way
of the extrapolation.
Error diagnosis is important, notably in real-time systems, to be able to
bring the real-time
system in a safe state, if needed. This is made possible when a coupling error
is ascertained
in the extrapolation, and method steps for treating the coupling error are
initiated in
dependence thereof.
The accuracy of the determination of the coupling variables can be improved
when, in
addition, methods for error compensation are used in the extrapolation.
In particular at the beginning of the simulation, it is possible that no
sufficiently accurate
model is yet available. This time period can be easily bridged by way of
signal-based
coupling to ascertain the coupling variables.
The accuracy of the extrapolation can be increased when a real-time bus system
is used
between a subsystem and the extrapolation unit, since the communication dead
time can be
accurately ascertained and consequently be compensated for more purposefully.
The present invention will be described in more detail hereafter with
reference to Figs.1 to 5,
which show advantageous embodiments of the invention by way of example and in
a
schematic and non-limiting manner. In the drawings:
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Fig.1 shows a signal-based extrapolation of the coupling variables according
to the
prior art;
Fig.2 shows the model-based extrapolation of the coupling variables according
to the
invention;
Fig.3 shows an exemplary flow chart of a method for extrapolating the coupling
variables;
Fig.4 shows an example of the co-simulation of an overall system; and
Fig.5 shows a simulation device for implementing the method for extrapolating
the
coupling variables.
For explanation, Fig.1 shows the signal-based approach to extrapolation of the
coupling
variables according to the prior art. Two subsystems TS1, TS2 are reciprocally
coupled. The
functions f1, f2 extrapolate the coupling variables yi, y2 from the input
variables x1, x2 by way
of polynomial extrapolation, such as zero order hold (ZOH), first order hold
(FOH) or second
order hold (SOH), which is to say y1=f1(x1(t), t), Y2=f2(x2(t),t).
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The following exemplary embodiment mentions two input, coupling and measured
variables,
respectively; however, the invention of course also covers any arbitrary other
number of such
variables.
According to the invention, a model-based approach is now chosen, in which a
mathematical
model M of the subsystems TS1, TS2 is used to extrapolate the coupling
variables yi, y2, as
shown schematically in FiG. 2. The model M is ascertained from the input
variables x1, x2
and/or from measured variables w1, w2, taking both the current and past time
values into
consideration. Input variables are generally understood to mean variables
that, for example,
can also correspond to data exchanged between simulation models. Measured
variables can
originate from sensors of any arbitrary type, for example, and signal noise
may accordingly
be present.
From the model M, yl=fi(xi(t), x2(t), t), y2=f2(x1(t), x2(t), t) follows for
the coupling variables.
When using only measured variables, y1=f1(w1(t), w2(t), t), Y2=f2(w1(t),
w2(t), t) follows for the
coupling variables from the model M in the exemplary embodiment shown. When
input and
measured variables are used according to the above-described definition,
yl=f1(xl(t), x2(t),
w2(t), t), y2=f2(x1(t), x2(t), w2(t), t)
follows for the coupling variables from the model
M.
Thus, a multiple-input, multiple-output (MIMO) system is present. Model M
includes an
identified model of the subsystems TS1, TS2 which is valid only locally, which
is to say short-
term for the current operating point of the overall system. By this model-
based extrapolation
the extrapolation is adaptively adapted to the system behavior or the system
solution.
However, the model-based extrapolation also allows noisy signals (coupling
variables yi, y2,
input variables xl, x2, measured variables wl, w2) to be processed since the
extrapolation is
carried out based on a model M, and is not based on the noisy measured
variables
themselves, which is not possible with signal-based extrapolation.
Sufficiently known methods of data-based model identification are resorted to
for determining
the model M. The model is ascertained from current and past input variables
xl, x2 and/or
measured values wl, w2 of the subsystems TS1, TS2. Such methods include, for
example,
recursive least squares methods (RLS, R Extended LS), (extended) Kalman filter
methods,
recursive instrumental variable methods, recursive subspace identification,
projection
algorithms, stochastic gradient algorithms, recursive pseudo-linear
regressions, recursive
prediction error methods, observer-based identification methods (sliding mode,
unknown
input observer, and the like), Fourier analysis, and correlation analysis.
Such methods are
used to determine and continuously optimize the parameters of the model M
based on the
current operating point of the overall system. The model structure can be
arbitrarily
predefined for this purpose, such as a second-order linear, time-invariant
system, having two
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inputs and outputs. The measured variables w1, w2 used are advantageously
measured
variables w1, w2 offered by the subsystems, wherein current and past measured
variables
w2 may be used.
An initial model may also be ascertained or predefined in advance at the
beginning of the
simulation using known quantities or external knowledge. So as to ascertain
the initial model
parameters, it is possible, for example, to backward calculate internal
starting states for the
subsystems and for the estimated model by way of inverse models, or to
calculate the
internal model states by way of a simpler method, until the model-based method
has reached
steady state, or it is possible to set correct starting values for the input
signals. However, in
principle, any arbitrary initial model may be used. It is also conceivable to
provide signal-
based coupling until the estimated model is available or valid.
Since the time behavior of the subsystems TS1 and TS2 for a certain time
period (operating
point) is known very well due to the model M, potential dead times can also be
compensated
for. In this way, the behavior of the respective other subsystem TS1, TS2 can
be predicted
without having to wait for the dynamic response of the system.
By using a model M to determine the coupling variables yi, y2, it is possible
to continue to
operate (at least temporarily) a real-time system error-free even in the case
of absent
measured variables w1, w2 over multiple coupling time steps, since these can
be reliably
determined by way of the model-based extrapolation.
The co-simulation of two subsystems TS1, TS2 can then take place as shown in
FiG.3. In a
first step according to the described exemplary embodiment, an initial model
is predefined or
ascertained. This is an optional step. Thereafter, in a second step, the
required measured
variables wi, w2 and/or input variables x1, x2 are read in and based thereon,
and in a third
step, the locally, which is to say within the simulation step, valid
parameters of the model M
are determined by way of a data-based method of model identification. The
parameters can
also remain valid over multiple simulation steps, for example when it is not
possible for some
reason to read in any new measured variables w1, w2 and/or input variables x1,
x2. Steps 2
and 3 would accordingly be eliminated.
Optionally, it is also possible to ascertain the coupling error, for example
an extrapolation
error, a dead time, absence of data, and so forth (step 4) and, based thereon,
method steps
may be initiated, such as aborting the simulation, switching the system to a
safe state, or
outputting a warning (step 8).
The model-based extrapolation allows the real and virtual dead times that
occur in the closed
system to be compensated for. The real dead time, caused by the communication
or the
signal exchange, such as via a bus system, but also by computing times, or
times for
measuring and processing the signals, can be compensated for by using the
model M to
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estimate further ahead into the future. Through the use of real-time bus
systems 4 (indicated
in FiG.5), which is to say time-triggered bus systems, or, generally speaking,
systems that
transmit time information in addition to the signal, the accuracy of the
extrapolation can be
increased since it is possible to exactly ascertain the communication dead
time, such as by
estimating the dead time based on the information from the real-time bus
system 4 or by
evaluating the estimated model. The virtual dead time, caused by time delays
as a result of
the sampling, can be implicitly compensated for through the use of the model-
based
extrapolation. The model-based extrapolation according to the invention can
thus be used to
compensate for all dead times, which results in a considerable improvement of
the simulation
behavior, notably when using real-time systems.
Based on the local model M, the coupling variables yi, y2 are calculated in a
fifth step, which
are then made available in a sixth step to the subsystems TS1, TS2 for the co-
simulation in
the next simulation step, whereby the method continues again with the second
step.
However, the coupling variables yl, y2 can also be further processed otherwise
in the
subsystems TS1, TS2, for example when a subsystem TS1, TS2 is not being
simulated, but
is really rigged up.
It is also possible to employ methods for additional error compensation in the
ascertainment
of the coupling variables yi, y2, such as a method as described in EP 2 442
248 Al. This
would allow the accuracy of the ascertained coupling variables yi, y2 to be
increased even
further.
FiG.4 shows a schematic illustration of the co-simulation of an overall system
1 using the
example of a hybrid vehicle. The subsystem TS1 represents an electric machine,
for
example, the subsystem TS2 an internal combustion engine, the subsystem TS3 a
drive
train, the subsystem TS4 an electrical energy storage, and the subsystem TS5 a
hybrid
control unit. The connections between these describe the connections between
the
subsystems TS. The hybrid control unit may be present in real, for example, in
HiL hardware,
and the other subsystems TS1 through TS4 run as simulations on appropriate
simulation
platforms, such as dSpace or Matlab, whereby real-time co-simulation becomes
necessary.
However, it is also possible to additionally configure other subsystems as
real hardware, for
example the internal combustion engine on an engine test stand.
FiG.5 shows the simulation device 3 for a portion of the co-simulation of the
overall system 1
by way of example. Each subsystem TSn is simulated in a dedicated simulation
environment
(hardware and with software for simulating the submodel of the subsystem using
the
intended solving algorithm) Sn. It is also possible, of course, to simulate
multiple or all
subsystems in one simulation environment. The simulation environment S5 is an
HiL system,
for example, comprising the corresponding hardware and software. The
simulation
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environments Si and S2 are realized on suitable computers, for example, with
appropriate
software, such as Simulink made by Mathworks or Adams made by MSC. The
subsystems
TS1 and TS5 are reciprocally dependent on each other, so that the dependency
for the co-
simulation must be resolved by way of the coupling variables yi, y2 as
described above. An
extrapolation unit 2 is provided for this purpose, which is implemented, for
example, as
computer hardware with appropriate software and the necessary algorithms, such
as for the
model identification. The extrapolation unit 2 receives the input variables
x1, x2 and measured
variable wl, w2 from the subsystems TS1, TS5 and, based thereon, identifies a
locally valid
model M for each simulation step. At the same time, the coupling variables yi,
y2 are then
calculated from the model M and made available to the subsystems TS1, TS5.
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